Preheat oven to 350 degrees F (175 degrees C). Grease two 8-inch round cake pans.

Blend cake mix, 1 1/3 cup pink Champagne, eggs, and vegetable oil together in a large bowl until moistened, about 1 minute. Add 3 tablespoons cherry juice and red food coloring; beat at medium speed until smooth, about 1 minute. Divide batter between cake pans.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, 29 to 34 minutes. Cool in the pans for 5 minutes. Invert onto wire racks and let cool completely, 25 to 30 minutes.

Beat heavy cream with an electric mixer until peaks form. Sprinkle white chocolate pudding mix over cream; beat until thoroughly mixed. Mix in 1 tablespoon confectioners' sugar and 1 tablespoon half-and-half until filling is smooth.

Spread filling over 1 cake layer and place second layer on top.

Beat 2 1/2 cups confectioners' sugar and butter together with an electric mixer until combined. Mix in 1/4 cup half-and-half, 2 tablespoons pink Champagne, 2 tablespoons cherry juice, and vanilla extract until frosting is smooth and spreadable.

Spread frosting over cake. Top cake with white chocolate shavings. Chill until serving.